Without more information about what you're trying to achieve, I'm just going to direct my answer to your apparent confusion regarding the difference between p-value and R-squared.
Significance is determined by your p-value. It appears that you have set your alpha to 0.10 (this is somewhat unusual - do you have justification for setting it this high?) so that means that any variable with a p-value less than 0.10 is going to show up as "significant". P-value is just a measure of the probability of getting a result as great or greater than what you observed, if the null were true. So for instance if your X variable actually had a p-value of 0.03, then 3% of the time running whatever data-collection you did you would "find" an X value that is as great as what you've observed, or greater (farther away from 0), even if the true value of X in real life IS zero. It's basically the risk you're taking of incorrectly concluding something (and with your significance level of .10, you've agreed to accept up to a 10% risk of a wrong conclusion).
R-squared measures the percent of variation in Y explained by variation in X (or combination of Xs - which is why we generally use adjusted R-squared so that throwing more unrelated variables in doesn't artificially and accidentally explain some of the variation when it really has nothing to do with Y). A high R-squared doesn't necessarily mean something is good, and a low one doesn't mean it is bad. In fact, a high R-squared with insignificant variables in the model doesn't tell you much at all. But a low R-squared with a well-built, significant model can tell you that you've discerned something interesting, even if it doesn't explain the whole picture. For another example, I am currently trying to figure out what environmental factors affect bacterial growth. I've built a model with some temperatures and salinity, and the R-squared is 0.19. 19% of the variation in bacterial growth explained by variation in temperature and salinity seems pretty good to me since we haven't yet included a lot of other possible environmental variables, and bacterial growth is complicated!
As a final (but most important) point, it's a red flag for someone to want to "show" that a particular variable is significant. It either is, or isn't - just as an independent variable either does or does not impact your dependent variable in real life. Manipulating your model to include a variety of conditions in order to achieve significance on one variable or another is heading into dangerous territory and I would avoid it at all cost. If you have an interest to keep reading, the first answer to this question explains well the problems with blindly changing things in a regression: Algorithms for automatic model selection